MIT Combinatorics Seminar Counting pattern avoiding permutations via integral operators Richard Ehrenborg  (University of Kentucky, visiting MIT) Friday, February 23, 2007    4:15 pm    Room 2-136 ABSTRACT A permutation is consecutive 123-avoiding if there are no three adjacent increasing elements. More generally, for S a collection of permutations on m+1 elements, this definition extends to define consecutive S-avoiding permutations. We show that the spectrum of an associated integral operator on the L2 space of the m-dimensional unit cube determines the asymptotics of the number of consecutive S-avoiding permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Krein and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde. This is joint work with Sergey Kitaev and Peter Perry.